There is an extension for Thunderbird called Thunderbird Conversations [1] for a conversation based UI that provides a look similar to Gmail (though it may not look like chat, which is possible and would look nice only for those who exchange short one or two sentence emails). As that addon says, "Don't forget to hit View > Sort By > Threaded in the menus." to use it. Perhaps this extension would help you.

[1]: https://addons.mozilla.org/en-US/thunderbird/addon/gmail-con...